Stabilizing Model Predictive Control for Nonlinear Systems in Input-Output quasi-LPV Form

Cisneros, Pablo S. G.; Werner, Herbert

doi:10.23919/acc.2019.8814342

Cited by 8 publications

(14 citation statements)

References 16 publications

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“…The states of the system are commonly the vector q q . To simplify the derivation of a qLPV representation of NL systems given by (22), consider the the transformed states given as follows…”

Section: Lpv Modeling Of a Class Of Nl Dynamicsmentioning

confidence: 99%

“…Note that (x,ū) belongs to the null space of the left matrix in (27); moreover, provided that the system is controllable for allp ∈ P, the dimension of the null space is n u . Now, consider qLPV models of the nonlinear dynamics (22) as illustrated in Section III and make use of the special structure in ( 26) with ( 25), we can rewrite (27) as…”

Section: Practical Lpvmpc For Reference Trackingmentioning

confidence: 99%

“…In this work, we consider the shoulder and the elbow corresponding to q 1 and q 2 , respectively, they are the most challenging links to control, since they are affected by gravity, inertial, centripetal, Coriolis and friction torques; the other links are fixed during the experiments. To demonstrate the quality of the proposed control approach we consider two practical trajectories [35] to be tracked and we compare with other MPC scheme developed recently in [22].…”

Section: Application To the Crs A465 Robotmentioning

confidence: 99%

“…Robust tracking MPC approaches for LPV systems have been developed recently in [19], which have achieved offset-free tracking for piecewise constant references. In [20]- [22] LPVMPC algorithms have been proposed for tracking time-varying reference trajectories, e.g., command trajectories in robotics applications. However, all these approaches cannot guarantee recursive feasibility of the associated MPC optimization problem.…”

Section: Introductionmentioning

confidence: 99%

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Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

et al. 2021

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In this paper, a practical model predictive control (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the linear parameter-varying (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single quadratic programming (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of admissible reference, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.INDEX TERMS Constrained systems, Linear parameter-varying systems, Model predictive control, Robust stability, Robotic manipulators.

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Section: Lpv Modeling Of a Class Of Nl Dynamicsmentioning

confidence: 99%

Section: Practical Lpvmpc For Reference Trackingmentioning

confidence: 99%

Section: Application To the Crs A465 Robotmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

et al. 2021

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“…A similar, yet more practical, approach to stabilizing MPC in tracking scenarios is to leverage the input‐output quasi‐LPV framework such that partitions are only necessary in the output space (which is lower dimensional). This issue has been studied and reported separately …”

Section: Trackingmentioning

confidence: 99%

Nonlinear model predictive control for models in quasi‐linear parameter varying form

Cisneros

Werner

2020

Intl J Robust & Nonlinear

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This article presents a nonlinear model predictive control (NMPC) approach based on quasi-linear parameter varying (quasi-LPV) representations of the model and constraints. Stability of the proposed algorithm is ensured by the offline solution of an optimization problem with linear matrix inequality constraints in conjunction with an online terminal state constraint. Furthermore, an iterative approach is presented with which the NMPC optimization problem can be handled by solving a series of Quadratic Programs at each time step, this being highly computationally efficient. A practical and simple way of obtaining quasi-LPV representations of the system using velocity-based linearization is presented in two examples. K E Y W O R D S efficient algorithms, linear matrix inequality, nonlinear model predictive control, quasi-linear parameter varying systems 1 Int J Robust Nonlinear Control. 2020;30:3945-3959.wileyonlinelibrary.com/journal/rnc

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An interpolation-based model predictive controller for input–output linear parameter varying systems

Hadian

Ramezani

Zhang

2022

Int. J. Dynam. Control

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Stabilizing Model Predictive Control for Nonlinear Systems in Input-Output quasi-LPV Form

Cited by 8 publications

References 16 publications

Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

Practical Model Predictive Control for a Class of Nonlinear Systems Using Linear Parameter-Varying Representations

Nonlinear model predictive control for models in quasi‐linear parameter varying form

An interpolation-based model predictive controller for input–output linear parameter varying systems

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